Model Identification 97

4.5 Methodology 94

4.5.3. Model Identification 97

The nature of SVAR requires imposition of enough restrictions so as to identify the orthogonal structural components of the error terms that are present in the shocks. Note that this is at variance to the standard recursive Cholesky orthogonalisation. The non- recursive orthogonalisation of the error terms produced through this process is used for the impulse response functions and variance decomposition.

For clarity, assume that 𝑦_𝑡is comprised of vector of endogenous variables. For example, say kth element of endogenous variables in our model where ∑ 𝐸[𝑣_𝑡𝑣́_𝑡] is the residual of the covariance matrix. Therefore, our identification procedure follows:

𝐴𝑣_𝑡 = 𝐵𝜇_𝑡 (4.7)

Where 𝑣_𝑡and 𝜇_𝑡 are vectors with lag length k, 𝑣_𝑡is the observed residual and 𝜇_𝑡 represents the unobservable structural innovations. A and B are k x k matrices which are to be estimated. However, innovation 𝜇𝑡 is assumed to be orthogonal in nature. Hence the covariance is an identity matrix𝐸[𝜇𝑡𝜇_𝑡^𝑡]=I. Imposition of restrictions on A and B is made possible due to the orthogonal assumption of 𝜇_𝑡. hence we have:

𝐴 ∑ 𝐴́=𝐵𝐵́ (4.8) The link between the reduced form and the structural form of the VAR model is presented as follows:

𝐵(𝐿) = 𝐵₀+ 𝐵⁺(𝐿) (4.9) 𝐴(𝐿) = −𝐵₀⁻¹𝐵⁺(𝐿) (4.10)

∑ =́ 𝐵₀⁻¹𝐴𝐵₀⁻¹ (4.11) Equation 6.9 is the structural form divided into contemporaneous correlations i.e𝐵0 and 𝐵⁺(𝐿).The former represents correlations at lag zero while the later represents correlations at all strictly positive lags. Equation 4.10 separates each reduced form coefficient into its structural counterpart 𝐵₀, identified through the reduced form,∑ =́ 𝐸[𝜇_𝑡𝜇_𝑡^𝑡], and the diagonal covariance matrix of the structural form, 𝐴 = 𝐸[𝑣_𝑡𝑣́_𝑡] as shown in 4.11.

Furthermore, due to the vulnerability of long run restrictions to serious misspecification problems, we use a contemporaneous restriction on the𝐵₀ matrix to identify the shocks as shown in equation 4.12 since this study is interested in short-run and medium term responses (see Leeper, Sims and Zha, 1996; Elbourne, 2007).

[ 𝑣^{𝑡𝑝𝑜𝑖𝑙}

𝑣_𝑡^{𝑜𝑖𝑙𝑔𝑟} 𝑣_𝑡^{𝑖𝑛𝑡𝑟} 𝑣_𝑡^{𝑚𝑠𝑔𝑟}

𝑣_𝑡^{𝑖𝑛𝑓𝑟} 𝑣_𝑡^𝑒𝑥𝑟 𝑣_𝑡^𝑚𝑔𝑟 𝑣_𝑡^{𝑔𝑑𝑝𝑔𝑟}]

=

[

1 0 0 0 0 0 0 0

𝐵₂₁⁰ 1 0 0 0 0 0 0

𝐵₃₁⁰ 0 1 0 0 0 0 𝐵₃₈⁰ 𝐵₄₁⁰ 0 𝐵₄₃⁰ 1 0 0 0 0

0 0 𝐵₅₃⁰ 𝐵₅₄⁰ 1 𝐵₅₆⁰ 0 0 𝐵₆₁⁰ 𝐵₆₂⁰ 0 0 𝐵₆₅⁰ 1 𝐵₆₇⁰ 0 𝐵₇₁⁰ 𝐵₇₂⁰ 𝐵₇₃⁰ 𝐵₇₄⁰ 𝐵₇₅⁰ 𝐵₇₆⁰ 1 0

0 0 0 0 𝐵₈₅⁰ 𝐵₈₆⁰ 0 1 ] [ 𝜇^{𝑡𝑝𝑜𝑖𝑙}

𝜇_𝑡^{𝑜𝑖𝑙𝑔𝑟} 𝜇_𝑡^{𝑖𝑛𝑡𝑟} 𝜇_𝑡^{𝑚𝑠𝑔𝑟}

𝜇_𝑡^{𝑖𝑛𝑓𝑟} 𝜇_𝑡^𝑒𝑥𝑟 𝜇_𝑡^𝑚𝑔𝑟 𝜇_𝑡^{𝑔𝑑𝑝𝑔𝑟}]

(4.12)

There are eight variables in the SVAR model namely oil price (poil) which is the exogenous variable.It occupies row 1 and it puts external pressure on the economy.

Endogenous variables are arranged as follows: oil resources growth rate (oilgr); interest rates (intr); money supply growth rate (msgr); inflation rate (inf); exchange rate (exr);

manufacturing output growth (mgr); and GDP growth rate (gdpgr). The role assigned to each variable is explained in the flow chart in figure 4.6

The oil price is viewed as the external shock to the entire system, meaning that it affects the monetary policy transmission mechanism MTM. The oil output growth rate is included in the MTM based on the controversy that often in oil exporting countries economic policies receive shock from the global oil price through the individual country’s oil output levels. Berument, etal (2004) in his study of Oman and UAE found that oil price shocks affect economic policies of these countries through their output levels. He argued that since these countries are heavily dependent on oil, the influence of oil prices on output is translated to economic wealth which dictates the behaviour of economic policies.

On the other hand, Jemenez and Rodriguez (2005) noted that most oil exporting countries run very open and liberal economies which make their economic policies highly susceptible to external shocks. They argued that as these countries are heavily dependent on oil, fluctuations in the global price of oil affect their economic policies without necessarily passing through their output levels.

The MTM comprises of the monetary policy instruments (MPIs) and the policy variables. The MPIs are interest rates and money supply growth rates. They are the operating targets (see Mahmud, 2009; Elborne, 2007). While the intermediate targets are the policy variables, namely inflation rate and exchange rate. They are viewed as an internal policy shock to the system (see Ushie, Adeniyi and Akongwale, 2012; Mordi and Adebiyi, 2010; Ngalawa and Viegi, 2011). The policy goals used are manufacturing output growth and GDP growth rate. Note that the manufacturing output growth is calculated as a percentage of GDP. The ordering of the variables follows Pesaran and Shin (1998) in order to overcome arbitrary ordering and likelihood of contemporaneous correlation.

The flow chart for the system is explained in figure 6.1. The MTM is the monetary policy transmission mechanism which involves the operating targets; the MPIs which are the interest rates and the money supply growth rates. It also includes the policy variables which are the intermediate targets, that is inflation rates and exchange rates.

Policy goals include manufacturing output growth and GDP growth rate.

The flow chart shows a schematic diagram of the monetary policy transmission mechanism (MTM). Firstly, there are the direct effect of the oil price shock on all the components in the model, which are oil growth rate, MTM, and outputs. Secondly, the diagram shows how the oil price shock passes through each of the components as they are arranged. Thirdly, we focus on the direct influence of the shocks in the MTM on the monetary policy goals; and finally we analyse how shocks in the MTM affect the variables in the model.

Figure 4.6 Flow chart for variables’ roles in the monetary transmission system

Oil Price Shocks

Oil Output Growth Rate

Outputs

MPIs

Policy Variables

MTM